There are 1 questions in this calculation: for each question, the 3 derivative of x is calculated.
    Note that variables are case sensitive.
\[ \begin{equation}\begin{split}[1/1]Find\ the\ third\ derivative\ of\ function\ {({x}^{16} + 3)}^{(\frac{5}{2})}\ with\ respect\ to\ x：\\\end{split}\end{equation} \]\[ \begin{equation}\begin{split}\\Solution:&\\ &Primitive\ function\ = (x^{16} + 3)^{\frac{5}{2}}\\&\color{blue}{The\ first\ derivative\ function：}\\&\frac{d\left( (x^{16} + 3)^{\frac{5}{2}}\right)}{dx}\\=&(\frac{5}{2}(x^{16} + 3)^{\frac{3}{2}}(16x^{15} + 0))\\=&40(x^{16} + 3)^{\frac{3}{2}}x^{15}\\\\ &\color{blue}{The\ second\ derivative\ of\ function:} \\&\frac{d\left( 40(x^{16} + 3)^{\frac{3}{2}}x^{15}\right)}{dx}\\=&40(\frac{3}{2}(x^{16} + 3)^{\frac{1}{2}}(16x^{15} + 0))x^{15} + 40(x^{16} + 3)^{\frac{3}{2}}*15x^{14}\\=&960(x^{16} + 3)^{\frac{1}{2}}x^{30} + 600(x^{16} + 3)^{\frac{3}{2}}x^{14}\\\\ &\color{blue}{The\ third\ derivative\ of\ function:} \\&\frac{d\left( 960(x^{16} + 3)^{\frac{1}{2}}x^{30} + 600(x^{16} + 3)^{\frac{3}{2}}x^{14}\right)}{dx}\\=&960(\frac{\frac{1}{2}(16x^{15} + 0)}{(x^{16} + 3)^{\frac{1}{2}}})x^{30} + 960(x^{16} + 3)^{\frac{1}{2}}*30x^{29} + 600(\frac{3}{2}(x^{16} + 3)^{\frac{1}{2}}(16x^{15} + 0))x^{14} + 600(x^{16} + 3)^{\frac{3}{2}}*14x^{13}\\=&\frac{7680x^{45}}{(x^{16} + 3)^{\frac{1}{2}}} + 43200(x^{16} + 3)^{\frac{1}{2}}x^{29} + 8400(x^{16} + 3)^{\frac{3}{2}}x^{13}\\ \end{split}\end{equation} \]

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